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arXiv · 1302.6000

A Generalization of the Hopf-Cole Transformation

Paulius Miskinis
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Abstract

A generalization of the Hopf-Cole transformation and its relation to the Burgers equation of integer order and the diffusion equation with quadratic nonlinearity are discussed. The explicit form of a particular analytical solution is presented. The existence of the travelling wave solution and the interaction of nonlocal perturbation are considered. The nonlocal generalizations of the one-dimensional diffusion equation with quadratic nonlinearity and of the Burgers equation are analyzed.

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Paulius Miskinis. 2013-02-25. A Generalization of the Hopf-Cole Transformation. https://doi.org/10.3842/sigma.2013.016

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